A198274 a(n) = 13*2^n-1.

12, 25, 51, 103, 207, 415, 831, 1663, 3327, 6655, 13311, 26623, 53247, 106495, 212991, 425983, 851967, 1703935, 3407871, 6815743, 13631487, 27262975, 54525951, 109051903, 218103807, 436207615, 872415231, 1744830463, 3489660927, 6979321855, 13958643711

Offset: 0

Author

Jeremy Gardiner, Oct 23 2011

Keywords

• nonn
• easy

Comments

a(n) + a(n-1)^2 = (a(n-1)+1)^2. - Vincenzo Librandi, Mar 24 2013

Examples

			a(2) = 13*2^2-1 = 51.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Gennady Eremin, Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant, arXiv:2405.16143 [math.CO], 2024. See pp. 3, 14.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A005029, A086224.

Programs

BASIC

for j = 0 to 30 : print str$((13*2^j)-1)+", "; : next j

Magma

[13*2^n-1: n in [0..30]]; // Vincenzo Librandi, Oct 28 2011

Mathematica

Table[13 2^n - 1, {n, 0, 30}] (* Vincenzo Librandi, Mar 24 2013 *)
LinearRecurrence[{3,-2},{12,25},40] (* Harvey P. Dale, Feb 06 2019 *)

PARI

a(n) = 13*2^n-1; \\ Michel Marcus, Jan 17 2016

Formula

a(n+1) = 2*a(n) + 1.

G.f.: ( 12-11*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 25 2011